Oisin this is what Wikepedia says
Today, the area has completely disappeared. Smithfield Markets expanded to become the Bull Ring Indoor Market was rebuilt and opened before the redevelopment of the Bullring Shopping Centre. Outdoor markets are held outside the entrance. The Bull Ring Rag Market was demolished as part of the development and a
multi-storey car park was constructed. The markets adopted the name of the Bull Ring and lost the Smithfield name. The original site of the Smithfield market is now Moat Lane car park. Smithfield Street, which connected Bradford Street (then Moat Row) to Digbeth High Street was renamed Mill Lane.[SUP]
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There are very few reminders of the existence of Smithfield. Smithfield House, an office building with ground floor retail, once occupied by Reddingtons Rare Records,[SUP]
[12][/SUP] bounded by Upper Mill Lane, Moat Lane and
Digbeth High Street is directly opposite the site of the old market. Inside the new multi-storey car park on Pershore Street is a walkway called Smithfield Passage.
The name of Moat Lane is a reference to the moat that once encircled the manor house on the site.